Design Example and Experiment

To show the feasibility of the proposed structure, an example is given below. The center frequency, in-band return loss, and fractional bandwidth of the filter are chosen to be 5GHz, 20dB, and 5% respectively. The filter is built on a Rogers RO4003 substrate withε_r =3.58, thickness=20mil, andtanδ =0.0021. The initial dimensions of the parallel-coupled filter are obtained by analytical method described in [7]. The coupling/shielding lines with length T1 and T2 are added at the ends of feed lines as shown in Figure 4-2, to introduce two transmission zeros separately. Two prescribed transmission zeros are located at 5.35GHz, and 5.7GHz respectively. The initial value of T1 and T2 can be arbitrarily set, say, T1=50 mil, T2=30 mil. The S-parameters of the filter is then obtained with the help of the commercial EM simulator Sonnet [32].

Next, the method described in chapter 2 can be used to extract the coupling matrix from the simulated S-parameters. The physical dimensions of filter are then adjusted

according to the extracted coupling matrix to match the prescribed response. After totally five of EM-simulation, matrix extraction, and physical parameters adjusting loops, one can get the simulated results as shown in Figure 4-3. The measured results are also shown in Figure 4-3 for comparison. The corresponding physical sizes are shown in Figure 4-2. And the corresponding coupling matrix M is extracted as follows

⎥ ⎥

Figure 4-3. Simulated and measured responses. Solid line: measured results. Dashed lines: EM simulated results.

It should be emphasized that filter shown in Figure 4-2 has exactly the same layout as the initial design except two coupling/shielding lines. So, designers can

easily realize this filter even by trial and error method without using of matrix extracting procedure.

Figure 4-4. EM simulated results of three different cases. The dimensions of the simulated filter are the same as these shown in Figure 4-2 except T2 is set to different values.

It is mentioned in section 4-2 that the introduction of the coupling/shielding lines in this way can effectively adjust the transmission zeros with slight perturbation of the passband return loss. To demonstrate the merits of easy tuning of the proposed structure, three EM simulations are taken in which the length of the coupling/shielding line, T2, are set to 14mil, 24mil, and 39mil respectively while the other dimensions are the same as these given in Figure 4-2. From the EM simulated results shown in Figure 4-4, it is obvious that the transmission zero can be tuned over a wide range with negligible change in the passband return loss.

Chapter 5 Microstrip Realization of Generalized Chebyshev Filters with Box-Like Coupling Schemes

In this chapter, generalized Chebyshev microstrip filters with box-like coupling schemes are presented. The box-like coupling schemes taken in this chapter include doublet, extended doublet, and fourth-order box-section. The box-like portion of the coupling schemes is implemented by an E-shaped resonator. Synthesis and realization procedures are described in detail. The example filters show an excellent match to the theoretical responses.

5.1 Introduction

The microstrip filters with generalized Chebyshev response attract considerable attention due to its lightweight, easy fabrication and ability to generate finite transmission zeros for sharp skirts. In the literature, most of them are based on cross-coupled schemes such as cascade trisection and cascade quadruplet. Some representative examples of cross-coupled microstrip filters are available in the book [12].

Recently, with the progress of the synthesis technique, new coupling schemes such as “doublet”, “extended doublet”, and “box-section” are introduced [38]-[40]. As shown in Figure 5-1, these coupling schemes have a box-like center portion, so we call them box-like coupling schemes. These coupling schemes impact the filter design since they do not only provide new design possibilities but exhibit some unique and attractive properties as well. They differ from the conventional cascade trisection and cascade quadruplet mainly on two aspects. First, there are two main paths for the signal from source to load while there is only one main path in the case of cascade trisection and cascade quadruplet. Second, the configuration of doublet and box-section exhibit the zero-shifting property which make it possible to shift transmission zero from one side of the passband to the other side simply by changing

the resonant frequencies of the resonator while keeping other coupling coefficients unchanged. The zero-shifting property implies that the similar physical layout can implement a filter with transmission zero at the lower stopband or at the upper stopband, which is not feasible on the conventional trisection configuration. Besides, the third-order extended-doublet configuration, as shown in Figure 5-1(b), exhibits one pair of finite transmission zeros as that of a cross-coupled quadruplet filter. Pairs of finite transmission zeros can be used to improve the selectivity of the filter or flatten the in-band group delay. However, to the author’s knowledge, only a few studies in the literature are focused on realization of the coupling schemes shown in Figure 5-1 with microstrip line [41], [42].

(a) (b)

(c)

Figure 5-1. Basic box-like coupling schemes for generalized Chebyshev-response filters discussed in this paper. (a) doublet. (b) extended doublet (c) box-section. ( The gray area is realized by the proposed E-shaped resonator)

An important property of the schemes in Figure 5-1 is that one of the coupling coefficients on the two main paths must be negative while others are positive. The simplest way to obtain the required negative sign is to use higher-order resonance [39], [42]. Unfortunately, higher-order resonance leads to a spurious resonance in the lower stopband. Instead of using higher-order resonance, loop resonators are arranged carefully to satisfy the required sign of coupling coefficients for the box-section configuration [41]. However, a similar method can not apply to doublet or extended-doublet. To overcome these difficulties, an E-shaped resonator as shown in Figure 5-2(a) is proposed to implement the required coupling signs.

(a) (b)

Figure 5-2. A doublet filter (a) the proposed layout (gray area indicate the E-shaped resonator) (b) the corresponding coupling scheme.

The E-shaped resonator can achieve the required magnitude and sign of the coupling schemes shown in Figure 5-1. As shown in Figure 5-2(a), the E-shaped resonator comprises a hairpin resonator and an open stub on its center plane. This symmetric

structure can support two modes: even mode and odd mode. Thus, the source and the load are coupled to both modes of the E-shaped resonator. That is even though only one physical path exists between source and load, there are two electrical paths between them. Consequently, the layout in Figure 5-2(a) can be modeled by the coupling scheme, a doublet, in Figure 5-2(b). The doublet filter illustrates how an E-shaped resonator directly couples to external feeding network.

Based on the proposed E-shaped resonator, filters with extended-doublet and box-section configuration can be realized as well. The E-shaped resonator can use either its even mode or odd mode to couple an extra resonator. Thus, the extended-doublet configuration in Figure 5-1(b) is achievable. Besides, the E-shaped resonator can couple to external resonators with two of its modes simultaneously and forms the box-section configuration in Figure 5-1(c). The feasibility of realization of the basic coupling schemes in Figure 5-1 with proposed E-shaped resonator makes it possible to realize a class of coupled microstrip filters in a unified approach.

5.2 Circuit Modeling